Can a skip trowel texture finish affect the overall straightness or linearity of a wall?

In my opinion, No it is not because of the wall texture.

The window jamb ( framing ) should have been installed to match the window frame regardless of weather or not the rough opening or the window was installed plumb and true. So your contractor is saying that the jamb was installed to match the window but the texture person put an uneven layer of texture mud resulting in a nearly 1/2" discrepancy. ?? ( unlikely ).

It is the foreman who is responsible for building a straight and plumb walls, a reasonably plumb and true rough opening and installing the window absolutely plumb and true.

Ultimately it is the contractor, the foreman's boss, who is responsible for the work being done.

Have you spoke with the contractor ?

I noticed that the newly constructed walls, not just the new window framing are crooked (vertically & horizontally along where our new baseboards are to be positioned).

If the foreman did not care enough to make the walls straight, plumb and true then they probably did not care enough to install the rough opening, window and jamb correctly.

Ask the contractor to explain and demonstrate how the texture is responsible for the problems you see in the sub-par quality of the construction. If you are not satisfied with the explanation than tell them you are going to hire a consultant to confirm the quality, or lack of quality, of the work.